https://file.aiquickdraw.com/mathbot/file/1726458047312tugxkx1o.jpg

The image shows a quadratic function \( f(x) = 6x^2 - 4x + 6 \) and asks for the values of \( f(x) \) at different points: \( f(-2) \), \( f(-1) \), \( f(0) \), \( f(1) \), and \( f(2) \).

We can compute these values by substituting each value of \( x \) into the function.

The function is: 
\[
f(x) = 6x^2 - 4x + 6
\]

### Calculation:
1. \( f(-2) = 6(-2)^2 - 4(-2) + 6 \)
2. \( f(-1) = 6(-1)^2 - 4(-1) + 6 \)
3. \( f(0) = 6(0)^2 - 4(0) + 6 \)
4. \( f(1) = 6(1)^2 - 4(1) + 6 \)
5. \( f(2) = 6(2)^2 - 4(2) + 6 \)

Let me calculate each of these.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can manually compute the values of \( f(x) \) using the equation \( f(x) = 6x^2 - 4x + 6 \). Substitute the given values of \( x \) (i.e., \( -2, -1, 0, 1, 2 \)) to calculate each.

Would you like me to guide you step by step on solving it manually? Let me know if you have any questions.

Here are 5 related questions you can try:
1. What is the vertex of the quadratic function \( f(x) = 6x^2 - 4x + 6 \)?
2. How would the graph of \( f(x) = 6x^2 - 4x + 6 \) look?
3. Can you rewrite \( f(x) = 6x^2 - 4x + 6 \) in vertex form?
4. How do you find the axis of symmetry for \( f(x) = 6x^2 - 4x + 6 \)?
5. What is the discriminant of \( f(x) = 6x^2 - 4x + 6 \), and what does it tell you about the roots?

**Tip:** When evaluating quadratic functions, always square the value of \( x \) first before performing other operations.

Given the function f(x) = 6x^2 - 4x + 6, calculate the following values: f(-2), f(-1), f(0), f(1), and f(2).

Learn how to evaluate the quadratic function f(x) = 6x^2 - 4x + 6 at different values of x, including -2, -1, 0, 1, and 2. This problem highlights core algebraic concepts suitable for students in Grades 7-10.

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